[1]} described linear time algorithms to find a stable matching in an instance of smi. These classical algorithms find either a man-optimal (or woman-optimal) stable matching in which every man (woman) is assigned to their best partner in any stable matching and every woman (man) is assigned to their worst partner in any stable matching. Favouring one set of agents over the other is often undesirable and so we look at the notion of a “fair" matching in which the happiness of both sets of agents is taken into account.
